LAM-PINN clusters PDE tasks via learning-affinity metrics and uses modular subnetworks to cut MSE by 19.7x on unseen tasks while using only 10% of conventional PINN training iterations.
One-shot transfer learn- ing of physics-informed neural networks
5 Pith papers cite this work, alongside 6 external citations. Polarity classification is still indexing.
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abstract
Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed Neural Networks (PINNs) to tackle such problems as they provide numerous benefits over traditional numerical approaches. Despite their potential benefits for solving differential equations, transfer learning has been under explored. In this study, we present a general framework for transfer learning PINNs that results in one-shot inference for linear systems of both ordinary and partial differential equations. This means that highly accurate solutions to many unknown differential equations can be obtained instantaneously without retraining an entire network. We demonstrate the efficacy of the proposed deep learning approach by solving several real-world problems, such as first- and second-order linear ordinary equations, the Poisson equation, and the time-dependent Schrodinger complex-value partial differential equation.
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A multihead PINN with orthogonalized linear heads learns low-dimensional latent embeddings of PDE solution families, with 2–4 principal components capturing 95% of latent variance for Burgers, heat, and wave equations.
Chebyshev polynomial surrogates enable one-shot closed-form adaptation of PINNs for a broader class of nonlinear ODEs and PDEs by decomposing them into linear subproblems.
Pi-PINN learns transferable physics-informed representations and solves known or unseen PDEs via closed-form pseudoinverse head adaptation, achieving 100-1000x faster predictions and 10-100x lower error than standard PINNs or data-driven models even with minimal training samples.
RealDiffusion uses heat diffusion as a dissipative prior and a region-aware stochastic process inside a training-free physics-informed attention mechanism to improve multi-character coherence while preserving narrative dynamism in sequential image generation.
citing papers explorer
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Compositional Meta-Learning for Mitigating Task Heterogeneity in Physics-Informed Neural Networks
LAM-PINN clusters PDE tasks via learning-affinity metrics and uses modular subnetworks to cut MSE by 19.7x on unseen tasks while using only 10% of conventional PINN training iterations.
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Physics-Informed Neural Embeddings of PDE Solution Families
A multihead PINN with orthogonalized linear heads learns low-dimensional latent embeddings of PDE solution families, with 2–4 principal components capturing 95% of latent variance for Burgers, heat, and wave equations.
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Chebyshev-Augmented One-Shot Transfer Learning for PINNs on Nonlinear Differential Equations
Chebyshev polynomial surrogates enable one-shot closed-form adaptation of PINNs for a broader class of nonlinear ODEs and PDEs by decomposing them into linear subproblems.
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Transferable Physics-Informed Representations via Closed-Form Head Adaptation
Pi-PINN learns transferable physics-informed representations and solves known or unseen PDEs via closed-form pseudoinverse head adaptation, achieving 100-1000x faster predictions and 10-100x lower error than standard PINNs or data-driven models even with minimal training samples.
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RealDiffusion: Physics-informed Attention for Multi-character Storybook Generation
RealDiffusion uses heat diffusion as a dissipative prior and a region-aware stochastic process inside a training-free physics-informed attention mechanism to improve multi-character coherence while preserving narrative dynamism in sequential image generation.